Question

Prove that the points A(-2,11), B(-6,-3), and C(4,9) form the vertices of a scalene triangle."

Options:
A. The distances between any pair of points are equal.
B. The sum of any two sides of the triangle is equal to the third side.
C. At least two sides of the triangle have the same length.
D. The lengths of the three sides of the triangle are different

Answer 1

To prove that the points A(-2,11), B(-6,-3), and C(4,9) form the vertices of a scalene triangle, calculate the lengths of the sides using the distance formula.

Step-by-step explanation:

To prove that the points A(-2,11), B(-6,-3), and C(4,9) form the vertices of a scalene triangle, we can calculate the lengths of the sides of the triangle.

The formula to find the distance between two points is d = √((x2 - x1)² + (y2 - y1)²). By calculating the distances AB, BC, and AC, we can determine if the lengths are different.

In this case, the distances are not equal, thus proving that the triangle formed by these points is scalene.